Theorems · Theorem · category theory

CategoryTheory.Triangulated.TStructure.eTriangleLTGE_distinguished

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
  [inst_2 : CategoryTheory.Limits.HasZeroObject C] [inst_3 : CategoryTheory.HasShift C ℤ]
  [inst_4 : ∀ (n : ℤ), (CategoryTheory.shiftFunctor C n).Additive] [inst_5 : CategoryTheory.Pretriangulated C]
  (t : CategoryTheory.Triangulated.TStructure C) (i : EInt) (X : C),
  (t.eTriangleLTGE.obj i).obj X ∈ CategoryTheory.Pretriangulated.distinguishedTriangles

Defined in: Mathlib.CategoryTheory.Triangulated.TStructure.ETrunc
Cited by: 1 results in Mathlib
Foundations: Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Preadditive CategoryTheory.Limits.HasZeroObject CategoryTheory.HasShift CategoryTheory.Functor.Additive CategoryTheory.Pretriangulated

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites23

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objstatement and proof · cited by 19,642
CategoryTheory.Functorstatement · cited by 16,252
Top.topproof · cited by 9,680
Bot.botproof · cited by 4,720
WithTopstatement · cited by 3,754
CategoryTheory.Preadditivestatement and proof · cited by 3,309
CategoryTheory.shiftFunctorstatement and proof · cited by 1,553
CategoryTheory.HasShiftstatement and proof · cited by 1,527
CategoryTheory.Limits.HasZeroObjectstatement and proof · cited by 1,298
CategoryTheory.Functor.Additivestatement and proof · cited by 1,179

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Triangulated.TStructure.triangleω₁δ_distinguishedproof · cited by 0